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Electrons on shrinkking surface

Anonymous Tue 05 Apr 14:55:19 2022 No.14366453 View Reply Original Report

Quoted By: >>14366634 >>14367349

What happens with electrons of an charged object in a vacuum, if we shrink it's surface without touching / discharging it ?

Anonymous

Anonymous Tue 05 Apr 2022 15:24:17 No.14366509 Report

Quoted By:

Can you explain how you'd do this to a conductor?

Anonymous

Anonymous Tue 05 Apr 2022 15:25:17 No.14366511 Report

Quoted By: >>14366527 >>14366528

3d electrostatics is really interesting in that for conductors are excess charge is confined to the surface of the conductor. this doesn't happen in 2d, where excess charge can be found inside the conductor.

it seems your situation is a stretchy sheet of insulator. in this case the electrons are confined to a surface, and if the geometry is scaled down, the positions of the electrons will also scale down. the end results is the distribution of electrons won't change (except for scale) and the surface charge density will go up (because charge is constant but area is going down)

Anonymous

Anonymous Tue 05 Apr 2022 15:28:46 No.14366527 Report

Quoted By: >>14366534

>>14366511
No shit. The 2d surface must have charge uniformly distributed everywhere. If charge were localized to the edges, you'd violate the uncertainty principle since you'd have infinite precision to one of its position coordinates.

Anonymous

Anonymous Tue 05 Apr 2022 15:29:17 No.14366528 Report

Quoted By:

>>14366511
but by electrophysics, isn't there a limit of how many electrons a surface can pick up before it's simply "full". and cannot further charged up ?

Anonymous

Anonymous Tue 05 Apr 2022 15:32:07 No.14366534 Report

Quoted By: >>14366540 >>14366542 >>14366554

>>14366527
it's a classical result that has nothing to do with QM.
physically surface charges are tightly confined to a surface but not actually 2d; you get exponential decay away from the surface.

Anonymous

Anonymous Tue 05 Apr 2022 15:34:17 No.14366540 Report

Quoted By:

>>14366534
So, do we then get a kind of beta ray then ?

Anonymous

Anonymous Tue 05 Apr 2022 15:35:12 No.14366542 Report

Quoted By: >>14366554

>>14366534
If it's classical, then is there a derivation for why charge isn't localized to the edges of a 2d sheet?

Anonymous

Anonymous Tue 05 Apr 2022 15:39:31 No.14366554 Report

Quoted By: >>14366637

>>14366534
>>14366542
I ask because the derivation for 3d conductors is pretty straightforward and contradicts your claim of 2d. In 3d, if the charges were not on the surface, there would be a net electric field inside the conductor, and hence a net force on the charges. Therefore it's not electrostatic. If we apply the same reasoning to the 2d case, we get electrons must be localized to the edges.

Anonymous

Anonymous Tue 05 Apr 2022 16:18:51 No.14366634 Report

Quoted By:

>>14366453
Electrons become closer to each other
Potential becomes higher due to coulomb force between charge carriers
This results in increasing voltage

Anonymous

Anonymous Tue 05 Apr 2022 16:18:57 No.14366637 Report

Quoted By: >>14366820

>>14366554
the potentials of a charge is different for different dimensions. in 3d the potential of a point charge is proportional to 1/r. in 2d the potential of a point charge is proportional to ln r.

i don't have time to prove this right now. maybe later.

Anonymous

Anonymous Tue 05 Apr 2022 17:18:25 No.14366820 Report

Quoted By:

>>14366637
That's valid, but I still don't see how the different forms of the potential have such totally different consequences

Anonymous

Anonymous Tue 05 Apr 2022 20:53:13 No.14367349 Report

Quoted By:

>>14366453
It shrinks until whatever force is compressing it is balanced by the electrostatic repulsion on the surface

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